Answer: This is kind of a long one. Good, though.

The current system of music notation is the result of a long evolutionary process, and it seems to me that, like the shape of a dolphin, it exists in its present form only because it was found to be efficient. There are alternative or at least supplementary systems, though, as I'll describe below.

There are basically two elements that one would need to record in keeping a record of music: pitch and rhythm. Pitch was originally notated roughly, just squiggles above written words to remind the singer where the melody rose and where it fell. Eventually these were made more precise with staff lines, and the innovations of the Ars Nova in the 14th century (see the connection?) added the ability to record rhythmic information as well. Since then we've had six more centuries of improvement, but the result follows the same principle as the earliest forms: musical tones are represented by graphical symbols whose vertical position tells their pitch and whose shape tells their rhythm.

One might complain that standard notation doesn't reveal all possible information: in actual performance musicians will stretch or contract the time here and there, and maybe even the pitch, but then the notation has the great advantage of being readable. The more information conveyed, the more difficult is the reading. Standard notation has apparently found a pretty good balance: it increases readability by assuming that the reader knows the basic scale steps represented by the staff and has a feeling for the beat (just imagine if it told the pitch in terms of frequency and the rhythm in terms of milliseconds!)

There are some alternatives, but the most successful tend to build on standard notation. Shape notes have the familiar staff lines and clefs and rhythmic system, but note heads come in triangles, squares, etc. to tell which scale tone is represented by that note. Shape notes have been shown to be useful in teaching children, and are traditionally used by adults in some churches, but shape notation is harder to write, especially by hand, and it has the disadvantage of being limited to music that stays in the major or minor scale. On the other hand, for simple music it can be written without staff lines. Even better, singers who know the solfege syllables can quickly learn to read the pitches, while those can read standard notation alone can ignore the shapes, so it has a real practical advantage in vocal music meant to be performed by untrained singers. Here's the start of Amazing Grace as presented in an old hymn book:

(We've added support for Shape Notes to Songworks with version 2.725. Songworks will automatically pick the correct shape for each note if you'd like to try printing music with shape notes - see the online user manual page on shape notes).

Tonic sol-fa is another alternative system with a considerable history, but it, too is less adaptable than standard notation. Tonic sol-fa can also be combined with standard notation, and uses only text symbols. The scale notes Do, Re, Mi, Fa, Sol, La, Ti are represented by their initials, while a system of colons, dashes, etc. tell the rhythm. This is of course less graphic than standard notation and I personally find it harder to read.

Though we have some useful additions to standard notation no one has come up with a system that works more efficiently, and I think this is another instance of organic evolutionary design winning over invention. It would take a real genius to come up with the shape and physiology of the dolphin, but nature accomplished this by trial and error. Current music notation was arrived at by a similar process of trial and error, and I think it's here to stay. From time to time improvements may appear, the innovations that work will be retained, and the system will continue to evolve as it always has, incrementally.

So the short version is no: I don't think there are other ways of writing music that work better to reveal pitch and rhythm. And if one were invented it would be very difficult to overcome the fact that millions of pages of music are written in the current system and millions of musicians know how to read them. But if one learns the basis of staff notation in a step-by-step manner, perhaps doing natural pitch first, then simple rhythm, then sharps and flats, more complex rhythm, etc., it is not so difficult a task as many imagine it to be.

UPDATE: exchange on this topic with one of our readers:

Q: Just a note. For question #10 your answer is misleading. There are MANY people who have come up with alternate notation systems that offer a lot of benefits over standard notation. These systems do not use accidentals or key signatures. They preserve visual intervals and chord shapes in every key. And align octaves in similar positions on the staff. All things that standard notation can not do. Take a look at www.mnma.org.

A: Thanks for the feedback. I'm aware of the chromatic notation systems - inventors have been trying to replace standard notation for many years - and the subject is one that can provide hours of entertaining argument. I should have made it more clear that there have been hundreds of such attempts, most of them aiming to eliminate the distinction between enharmonics like D# and Eb, to eliminate accidentals and key signatures, and to make the same note names appear identical in all octaves. For the benefit of the audience, here is the way two prominant chromatic systems would represent a c minor triad, then a non-triadic C-D#-E, and finally a C major triad:

A chromatic system that cycles on the octave (every pitch looks the same in every octave) is in theory very attractive from the easy-to-play angle. Certainly some of the many, many variations on this idea are rational, some are elegant, and the simplest of these have none of the quirks of the standard system.

But for me the charm of the standard system lies in those very quirks, because they reflect the system's organic basis in tonality. The standard system is an image of the history of tonal music, and expresses the nature of tonality in its irregular step patterns, its insistence on enharmonic distinctions, etc. And that does have one practical benefit, which is that the harmonic meaning of a passage is evident in its notation. If I am reading a passage in which Sol is followed by a sharped Sol, that has a different meaning for me than Sol moving to a flat La, one that may even influence pitch on a continuously variable-pitch instrument like the violin. I feel the sense of a probable secondary dominant on the sharp Sol, something like a minor subdominant on a flat La. A chromatic system, though beautifully rational for atonal music played in equal temperament, doesn't convey these tonal hints because a sharp Sol and a flat La are notated exactly the same way. Similarly, the standard system gives a special significance to the triad, which when written with the correct enharmonics always appears as three tones on adjacent lines or adjacent spaces, whether it is major or minor. The triad keeps the same visual form because that is a natural consequence of the staff system being based on a diatonic scale.

Another way of putting that comes from information theory: the standard system contains more information. Chromatic notation systems achieve their benefits by removing the information contained in the enharmonic distinctions of standard notation. That is OK only if one doesn't value that missing information, but I do value it. An Ab dominant seventh triad has a meaning distinct from that of a 'German' augmented 6th chord on Ab, but in chromatic notation the two are identical. None of that would matter if the world gave up tonality,but tonality is going to remain with us.

Shape notes, mentioned above, are an example of an organic extension to standard notation that adds information rather than subtracting it. But they enable the reader, at least in simple diatonic music, to ignore the pitch information contained in the standard system - which is still present - and to read only the meaning of the shapes. Shape notation has succeeded and endured, I think, because it leaves intact the information of standard notation; it's an add-on.

Reasonable people can disagree on the relative benefits of alternate systems, many of which are very clever, but in the end we must also deal with the practical problem of replacing a system known by perhaps hundreds of millions of people and enshrined in millions of printed scores and parts. It isn't going to go away; it will gradually evolve as it always has; future variations will be "backward compatible" with existing scores: those who know the latest evolution will still be able to read the older ones.

You could compare this dispute with that over artificial languages such as Esperanto. Esperanto is well-designed, rational, much easier to learn than any natural organic language full of quirks acquired over years of evolution. But it also lacks the cultural information carried by those missing quirks; it is not rich. Absent any world dictator with the power to force people to use Esperanto they continue to speak and read in the naturally evolved languages, and they always will.